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Neutron-proton elliptic flow difference and ratio have been shown to be promising observables in the attempt to constrain the density dependence of the symmetry energy above the saturation point from heavy-ion collision data. Their dependence on model parameters like microscopic nucleon-nucleon cross-sections, compressibility of nuclear matter, optical potential, and symmetry energy parametrization is thoroughly studied. By using a parametrization of the symmetry energy derived from the momentum dependent Gogny force in conjunction with the T\'{u}bingen QMD model and comparing with the experimental FOPI/LAND data for 197Au+197Au collisions at 400 MeV/nucleon, a moderately stiff, x=-1.35 +/- 1.25, symmetry energy is extracted, a result that agrees with that of a similar study that employed the UrQMD transport model and a momentum independent power-law parametrization of the symmetry energy. This contrasts with diverging results extracted from the FOPI $\pi^{-}/\pi^{+}$ ratio available in the literature

Recent data from the NA49 experiment on directed and elliptic flow for Pb+Pb reactions at CERN-SPS are compared to calculations with a hadron-string transport model, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The rapidity and transverse momentum dependence of the directed and elliptic flow, i.e. v1 and v2, are investigated. The flow results are compared to data at three different centrality bins. Generally, a reasonable agreement between the data and the calculations is found. Furthermore, the energy excitation functions of v1 and v2 from E beam = 90A MeV to Ecm = 200A GeV are explored within the UrQMD framework and discussed in the context of the available data. It is found that, in the energy regime below E beam ≤ 10A GeV, the inclusion of nuclear potentials is necessary to describe the data. Above 40A GeV beam energy, the UrQMD model starts to underestimate the elliptic flow. Around the same energy the slope of the rapidity spectra of the proton directed flow develops negative values. This effect is known as the third flow component ("antiflow") and cannot be reproduced by the transport model. These differences can possibly be explained by assuming a phase transition from hadron gas to quark gluon plasma at about 40A GeV.

The nuclear stopping, the elliptic flow, and the HBT interferometry are calculated by the UrQMD transport model, in which potentials for "pre-formed" particles (string fragments) from color fluxtube fragmentation as well as for confined particles are considered. This description provides stronger pressure at the early stage and describes these observables better than the default cascade mode (where the "pre-formed" particles from string fragmentation are treated to be free-streaming). It should be stressed that the inclusion of potential interactions pushes down the calculated HBT radius RO and pulls up the RS so that the HBT time-related puzzle disappears throughout the energies from AGS, SPS, to RHIC.PACS numbers: 25.75. Gz,25.75.Dw,24.10.Lx One of the most important discoveries from SPS and RHIC experiments in the beginning of this century is that a new form of matter is produced in high energy ion collisions that seems to behave as a strongly interacting quark gluon plasma (sQGP) [1,2,3,4]. Furthermore, at RHIC energies, the sQGP seems to be a nearly "perfect liquid" with small viscosity [5,6]. Although hydrodynamical studies are a useful tool for the theoretical investigations at RHIC energies, hydrodynamics fails at lower energies. Therefore, a relativistic dynamic transport approach, in which an entire equilibrium is not pre-assumed, is necessary to explore the excitation functions of various observables. In addition, the transport model has the advantage of observing the whole phase-space evolution of all particles involved in a microscopic fashion.In order to detect this new matter -quark gluon plasma (QGP) -many theoretical suggested observables have been discussed and argued frequently. Among these, the Hanbury-Brown-Twiss interferometry (HBT) or Femtoscopy technique has been used widely to extract the spatio-temporal information of the particle freeze-out source. It would be a vital discovery if there is an nontrivial transition in the spatio-temporal characteristics of the source, when going from low to high beam energies [7]. Experimentally, the HBT parameters have been scanned thoroughly over the energies from SIS, AGS, SPS, up to RHIC, unfortunately, no obvious discontinuities do appear [8].However, this "null" result does not mean that the HBT technique comes to an end. Non-Gaussian effects * E-mail address: liqf@fias.uni-frankfurt.de might shadow the possible energy dependence of the HBT parameters ("E-puzzle"), and this topic has been quickly improving in the recent years [9,10,11]. Secondly, even with a Gaussian parametrization, we found that the HBT time-related puzzle ("t-puzzle") is present at almost all energies from AGS to RHIC [12]. In order to understand the origins of these "puzzles", it is necessary to dig deeper into the dynamics of the heavy ion collisions.The hydrodynamic model, in which various kinds of equations of state (EoS) with latent heats are considered, successfully explained the elliptic flow v 2 at transverse momentum p t < 2GeV/c at RHIC energies [13,14,15]. However,...